Contents

pp v-xi

Preface to first edition

pp xii-xx

Preface to second edition

pp xxi-xxi

Glossary

pp xxii-xxiv

PART I - NUMBERS

pp 1-2

1 - Mathematical induction

pp 3-9

2 - Inequalities

pp 10-27

3 - Sequences: a first bite at infinity

pp 28-67

4 - Completeness: what the rational numbers lack

pp 68-103

5 - Series: infinite sums

pp 104-140

PART II - FUNCTIONS

pp 141-142

6 - Functions and continuity: neighbourhoods, limits of functions

pp 143-181

7 - Continuity and completeness: functions on intervals

pp 182-202

8 - Derivatives: tangents

pp 203-223

9 - Differentiation and completeness: Mean Value Theorems, Taylor's Theorem

pp 224-250

10 - Integration: the Fundamental Theorem of Calculus

pp 251-285

11 - Indices and circle functions

pp 286-308

12 - Sequences of functions

pp 309-334

Appendix 1 - Properties of the real numbers

pp 335-339

Appendix 2 - Geometry and intuition

pp 340-341

Appendix 3 - Questions for student investigation and discussion

pp 342-345

Bibliography

pp 346-350

Index

pp 351-356